Current mode bandgap reference circuits are widely used in integrated circuits to provide a reference current that is compensated for variation in temperature. In a current mode bandgap reference circuit a current is generated that is a weighted sum of a component that is proportional to a bipolar transistor base-to-emitter voltage (Vbe) and a component that is proportional to a difference of Vbe's, referred to as ΔVbe, or delta Vbe. A reference voltage having a selected value may be produced from such a current by mirroring it into a resistor, with the mirror gain and resistor value chosen to produce the desired voltage. Such an approach has become increasingly popular, since many modern scaled CMOS processes cannot accommodate the normal voltage-mode bandgap voltage of approximately 1.2 volts.
The reason for the choice of current components in a current-mode bandgap reference circuit is the same for a voltage-mode reference circuit, that is, to combine the negative temperature coefficient of a Vbe with the positive temperature coefficient (proportional to absolute temperature, or, PTAT) of a ΔVbe, so as to obtain a current that has an average temperature coefficient of zero, or some other desired value, over a target temperature range, hereinafter referred to as the bandgap current. Note that the ΔVbe is defined as the difference in the Vbes of two transistors that have emitter current densities of a known ratio (diodes can also be used). The current components can be obtained in a circuit by applying the Vbe and ΔVbe voltages across resistors. If these resistors and the resistor used to convert the total current to a reference voltage are all internal to a particular integrated circuit (IC), they can be expected to have been all processed the same. Thus, their absolute values will track from IC to IC, and the temperature coefficient of the reference voltage will depend only on resistor and transistor ratios, and on transistor characteristics that are relatively process-insensitive.
The equation for a reference voltage provided by a current-mode bandgap reference circuit as described above is:Vref=Ibg*Ro,  Eq. (1)where Vref is the reference voltage output by the circuit, Ibg is the bandgap current and Ro is the output resistor used to convert the bandgap current to the reference voltage. Equation (1) may be expanded:Vref=(Vbe/Rvbe+ΔVbe/Rdvbe)*Ro,  Eq. (2)where Vbe is the base-emitter junction voltage of the negative temperature coefficient contributor transistor, Rvbe is the value of the resistor(s) providing the negative temperature coefficient current contribution, ΔVbe is the delta Vbe of the circuit and Rdvbe is the value of the resistor in the current path providing the PTAT current contribution. The resistor values in Equation (2) may be expressed as device-area-related constants multiplied by the process-sensitive resistivity p of the resistor material. Expanding Equation (2) in this way results in:Vref=(Vbe/(Kvbe*ρ)+ΔVbe/(Kdvbe*ρ))*(Ko*ρ),  Eq. (3)where Kvbe is the device-area-related constant for the resistor(s) providing the negative temperature coefficient current contribution, Kdvbe is the device-area-related constant for the resistor in the current path providing the PTAT current contribution, and Ko is the device-area-related constant for the output resistor used to convert the bandgap current to the reference voltage. It can be seen that in Equation (3) the resistivity factor ρ cancels out, resulting in:Vref=(Vbe/Kvbe+ΔVbe/Kdvbe)*Ko,  Eq. (4)
An example of a current-mode bandgap reference circuit that implements this equation, using diodes, is described in A CMOS Bangap Reference Circuit with Sub-1-V Operation, by H. Banba, et al., IEEE Journal of Solid-State Circuits, Vol. 34, No. 5 (May 1999), pp. 670-674, which is incorporated by reference herein. Another example, using bipolar transistors and having curvature compensation, is described in Curvature-Compensated BiCMOS Bandgap with 1-V Supply Voltage, by P. Malcovati, et al., IEEE Journal of Solid-State Circuits, Vol. 36, No. 7 (July 2001), pp. 1076-1081, and which is also incorporated by reference herein. FIG. 1 is a circuit diagram of the current-mode bandgap reference circuit described in the Malcovati et al. article. Comparing the designations in the above equations with the designations in this circuit, R3 corresponds to Ro, R1 (and R2) corresponds to Rvbe, R0 corresponds to Rdvbe and Q1 is the bipolar transistor determining Vbe, with ΔVbe being determined by the difference between the Vbe's of bipolar transistors Q1 and Q2, the emitter areas of which have a ratio of 1:N. Devices M1, M2 and M3 are PFET transistors configured to mirror current I1 through device M3, i.e., I1=I2=I3.
It was mentioned above that the K values in the above equations are device-area-related constants. Specifically, Kvbe, Kdvbe and Ko are expressed as resistor layout ratios, and are relatively process-insensitive. The ratio of bipolar base-emitter current densities that is used to determine ΔVbe is also based substantially on layout geometries. The Vbe term, however, exhibits sensitivity to process variations that is significant in many applications.
A major portion of the variation of Vref due to variation of Vbe is not due to variation in the processing of the bipolar transistors, but, rather, in the variation of Vbe as a function of the resistor resistivity, ρ. The reason for this Vbe variation is that the absolute values of the currents in the bipolar transistors are set by ΔVbe divided by Rdvbe, i.e., the value of resistor R0 in FIG. 1. Referring now to FIG. 1, the following equations apply:Vbe1=(kT/q)*In (le1/ls),  Eq. (5)where Vbe1 is the base-emitter junction voltage of transistor Q1, kT/q is the thermal voltage VT of transistor Q1 (k is Boltzmann's constant, T is absolute temperature and q is the charge of an electron), Ie1 is the emitter current of transistor Q1 and Is is the saturation current of a base-emitter junction for the process used to fabricate the circuit of FIG. 1. Since Ie1=Ie2, Equation (5) may be expressed as:Vbe1=(kT/q)*ln(Ie2/Is)=(kT/q)*ln((ΔVbe/R0)/Is),  Eq. (6)where R0 is the value of resistor R0. Applying Equation (6) to Equation (4) yields:Vref=((kT/q)*ln((ΔVbe/(Kdvbe*ρ))/Is)/Kvbe+ΔVbe/Kdvbe)*Ko  Eq. (7)
Illustrating Equation (7) quantitatively, assume that the resistor values are chosen so that Vref is a standard bandgap voltage of approximately 1.2 volts. In such a case, Ko/Kvbe is 1, meaning that the small signal gain from Vbe to Vref is 1. Equation (7) shows that Vbe varies as (kT/q)*ln(1/ρ). If kT/q is 0.026 volts and ρ varies by plus or minus 30%, then the variation in Vref over this variation in ρ can be expressed as:ΔVref(ρ+/−30%)=(kT/q)*ln(1.3/0.7)=0.026*ln(1.86)=16 mV.  Eq. (8)
This is a variation of approximately +/−1.3% for a Vref of 1.2 volts. If Vref is used for signal amplitudes, this represents a variation of approximately +/−0.06 dB. In some applications, the gain tolerance allocated to one stage of a signal path can be 0.1 dB or lower. Thus, this source of variation in Vref may be unacceptable in such applications.